permutations and combinations (1 Viewer)

[jnney]

there is a 3 lock code with 8 different letters. suppose the lock operates by holding 3 buttons together so that order is not important. how many codes are possible?

why isnt the answer 8C3 x 7C2 x 6C1?

 

[iwantfreeessays]

Does each lock have 8 letters on it? 8*8*8

 

[jnney]

There is only one lock.

 

[Shadowdude]

there is a 3 lock code with 8 different letters. suppose the lock operates by holding 3 buttons together so that order is not important. how many codes are possible?

why isnt the answer 8C3 x 7C2 x 6C1?

Your question isn't clear.

Your answer would have this sort of logic, however:

1. Pick three letters from eight... C(8,3) ways
2. Pick two letters from seven... C(7,2) ways
3. Pick one letter from six... C(6,1) = 6 ways

Which is clearly wrong.

That sort of answer implies there are three locks, and you pick three 'letters' from the first lock which has 8 to choose from, two from the second which has seven letters and one from the third which has six.

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Now if your question is: "There is a lock with eight letters and three of them must be pushed down to unlock it. How many codes are possible?"

The answer is 8*7*6.

Answer:

1. Pick the first letter as part of the combination... 8 ways
2. Pick the second letter for the combination... 7 ways (as we can't select the same letter twice)
3. Pick the third letter for the combination... 6 ways (by similar reasoning).

So 8 x 7 x 6 is the answer.

 

[Shadowdude]

What's the question? Word for word.

EDIT: Okay, okay now I get it.

You said order is NOT important, which means if the 'letters' were A, B, C, D, E, F, G and H - then ABC is the same as pressing BCA or CAB. I counted those separately but they are in fact the same thing.

In that case, the solution is easier.

1. Select three letters from eight... C(8,3) ways

And "8C3" is 56.

 

[jnney]

but isnt 8 x 7 x 6 different from 8P2?

8x7x6 gives 336

 

[iwantfreeessays]

You may have the order/unorderd thing wrong.

unorderd=8*7*6/3*2*1=56

 

[jnney]

A security lock has 8 buttons. Each person using the lock is given a 3-letter code. Now suppose that the lock operates by holding 3 buttons down together, so that order is NOT important. How many different codes are possible?

 

[Shadowdude]

but isnt 8 x 7 x 6 different from 8P2?

8x7x6 gives 336

Oh wait.. yes it is. My bad. This is what happens if you do maths late at night.

I'll edit it now...

Remark: P(8,3) = 336 = 8*7*6, but that might be a little confusing so I left it just as 8*7*6

A security lock has 8 buttons. Each person using the lock is given a 3-letter code. Now suppose that the lock operates by holding 3 buttons down together, so that order is NOT important. How many different codes are possible?

Yep, see what I posted above. But that is kinda poorly worded, I have to admit. Fault of the textbook maker.

 

[jnney]

thank you

 

[someth1ng]

It's just 8C3 because there are 8 buttons that can be pressed and you must press 3. Basically, how many ways can you pick 3 letters from a group of 8.